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Berlin, Staatsbibliothek Preußischer Kulturbesitz, lat. fol. 246

Date:

s. XV^med (1444 for the Ptolemaic section, cf. explicit; most of the MS was copied from 1443 to 1447 (cf., e.g., f. 23vb, 31vb, 47vb, 81rb, 154vb, 175ra, 184vb, 239vb, 252va and 258ra), with sections added at a later stage, as is the case for f. 94v-108v, copied in 1458, cf. f. 101ra).

Or.:

notebook of Ludolph Bochtorp, who was successively student at the University of Erfurt (where he received his master of arts in 1445), student in medicine at the University of Padua and physician in Brunswick (Braunschweig), cf. f. 1r: ‘In presenti volumine continentur infrascripte materie 54, quas omnes ego Ludolphus de Borchtorpe manu propria scripsi, exceptis questionibus spere et rithmimachia, Erfordie, Padue et in Brunsco… (?)’; f. 23vb: ‘… quando ego Ludolfus Borchtorp artis baccalaureus… anno 1445… promotus fui in magistrum artium liberalium Erfordie’; f. 154vb: ‘Et sic est finis huius lecture finite per me Hinricum Brunswik in studio Erfordensi pro honorabili viro magistro Ludolfo Borchtorp de Brunswik anno domini 1445 incompleto…’).

Prov.:

the MS was purchased in 1479 by one ‘Tile de Strobel (?)’, cf. note at the top of f. 1r. The same hand left an astronomical note in the margin of f. 59v: ‘Inveni ego T. de S. … anno 1480 incompleto…’.

Paper, 263 f., one main hand (Ludolph Bochtorp), except for f. 2^bisra-24v and 206r-215v, copied by two other hands.

Astronomy, astrology and computus: scattered astronomical notes and diagrams (inner front cover); table of contents (1r); astronomical notes and diagrams (1v-2v), including ‘Ptholomeus natus fuit in Alexandria…’ (2rb); ‘<Ci>rca textum spere materialis que utur primo … (?) diffinitio spere. Utrum diffinitio spere prima in textu posita sit bona. Quia dicitur spera est transitus circumferentie dimidii…’ (2^bisra-22rb); Heinricus Runen, Questio de celebratione Pasche (22va-23vb); Ptolemaica (24ra-31vb); Pseudo-Messahallah, De compositione astrolabii (32r-38vb); canons of Toledan tables (39ra-45vb); ‘Imagines celi numero 48 reperiuntur… Et sic completur tractatus de 48 ymaginibus celi’ (46ra-47vb); Theorica planetarum Gerardi (48r-52v); John of Ligneres, Algorismus de minutiis (53r-56r); Robertus Anglicus, Quadrans vetus (56v-59r); Pseudo-Messahallah, De compositione astrolabii, first chapter only (59r); solar tables (59v-60v); star table and shadow table (60v); Cristannus de Prachaticz, Usus astrolabii (61r-66v); Cristannus de Prachaticz, Compositio astrolabii (66v-70r); ‘Ad componendum horarium Achas fiat semicirculus…’ (70r); Johannes Eligerus de Gondersleuen, De utilitate quadrantis (70v-73r); ‘Cum visis fueris tibi formare equatorium…’ (73r-74r); ‘In compositione chilindri quod horologium viatorum vocatur. Accipe lignum durum…’ (74r-74v); ‘Ad sciendum figuram in qua faciliter invenitur vera coniunctio…’ (75r); Pseudo-Albertus Magnus, Speculum astronomie (75va-79va); ‘Quando videntur aliqua signa in Sole…’ (79va); John of Murs, Tabula tabularum, canons (79vb-81rb); notes of arithmetic (81rb); Franco de Polonia, Tractatus de turketo (81va-82ra); ‘In confectione virge visorie accipe circinum…’ (82ra-82va); ‘Ad conficiendum artificialiter baculum Iacob…’ (82va); Johannes de Harelbeke, Tractatus de spera solida (82vb-86v); ‘Notandum quod omnes regule mensurationum (?) sive in altum…’ (86v); Blasius of Parma, Demonstrationes in theorica planetarum (87ra-93vb); ‘De latitudinibus planetarum. Latitudo planete nichil aliud est…’ (94ra-94rb); Hermann Zoest, Phaselexis (94va-101ra); excerpt on calendar reform from 1437 ‘Sacrosancta generalis sinodus Basiliensis…’ (101ra-101va); Hermann Zoest, Kalendarium Hebraicum novum (101vb-108v); ‘De mensuratione terre et corporum celestium. Investigantes secundum famosiores…’ (109ra-110va); ‘Pro constituendis horariis in parietibus elevatis…’ (110vb-111va); Messahallah, De mercibus (111vb-113ra); Abraham Avenezra, De mundo vel seculo, tr. Henry Bate of Mechelen, excerpts ‘Extracta quedam ex Abraham Iudeo. Ex libro revolutionum Abrahe habetur quod…’ (113ra-113vb); John of Saxony, Canones (114ra-121rb), with additions mentioning the years 1440-1443 (121rb-121vb); Alfonsine tables (122r-143v); John of Sicily, comm. on the canons of the Toledan tables (144ra-154vb); ‘Excerptum tractatus de mensurationibus Iohannis de Lineriis. Profunditatem putei mensurare, fac 2 signa…’ (155ra-155rb); geographical coordinates of cities (155v); Petrus de Sancto Audomaro, Quadrans novus (156r-157r); computus table (157v); Henricus Selder, Canones tabularum Alphonsinarum (158r-175r); Alcabitius, Introductorius (175va-184vb); Thaddeus of Parma, Expositio super theorica planetarum (185ra-205ra); ‘Ad inveniendum ascensionem cuiuslibet gradus zodiaci a capite equinoxialis…’ (205ra-205va); ‘Notandum quod h… (?) vel terra in tres partes…’ (205vb); ‘Incipit tractatus rithmimathie, id est pugna numerorum ars pulchra. Quoniam igitur huius artis scientia ab ignorantibus contempnitur…’ (206ra-215v); Leopold of Austria, De astrorum scientia (216ra-239vb); Zael, Liber iudiciorum (240ra-252va, Introductorium, Quinquaginta precepta and De interrogationibus); Guillelmus Anglicus, De urina non visa (252vb-253vb); ‘Si quis voluerit scire quod sit in quolibet mense ex pluviis et ventis et qualitatibus temporis…’ (254ra-254va); ‘Incipit Hali de Luna. Luna cum fuerit in prima domo significat principatum et effectum rerum…’ (254va-255ra); circular diagram: aspects (255r); table: elections from the aspects of the Moon with the other planets (255r); astrological tables: 12 signes, essential dignities and degrees (255v-256v); Astronomia Ypocratis (257ra-258ra); Zael, Liber iudiciorum (258rb-261vb, De electionibus and Liber temporum); table of equation of houses for latitude 52° (262r-263r); ‘Invectiva contra astronugos et specialiter contra quendam rudem et presumptuosum. Quos universi scientie astrorum veri amatores…’ (263va-263vb); scattered astronomical notes (inner back cover).

Bibl. E. Zinner, ‘Aus alten Handschriften’, Naturforschende Gesellschaft Bamberg 38 (1962), 8-57: 14-17; P. Zambelli, S. Caroti, M. Pereira, S. Zamponi, Alberto magno: Speculum astronomiae, Pisa, 1977, 102-104; M. Folkerts, ‘Mittelalterliche mathematische Handschriften in westlichen Sprachen in der Berliner Staatsbibliothek. Ein vorläufiges Verzeichnis’, in Mathematical Perspectives. Essays on Mathematics and Its Historical Development Presented to Kurt-Reinhard Biermann on the Occasion of His 60^th Birthday, ed. J. W. Dauben, New York, 1981, 53-93: 63-65; P. O. Kristeller, Iter Italicum, III, London-Leiden, 1983, 481; P. O. Kristeller, Iter Italicum, VI, London-Leiden, 1992, 497; O. de Solan, ‘La réforme du calendrier dans une question quodlibétique de Henri de Runen (1444)’, Bibliothèque de l’École des Chartes 157 (1999), 171-220: 180-182; R. Lemay, Le Kitāb aṯ-Ṯamara (Liber fructus, Centiloquium) d’Abū Jaʿfar Aḥmad ibn Yūsuf [Ps.-Ptolémée], 1999 [unpublished], I, 284-287; A. Paravicini Bagliani, Le Speculum Astronomiae, une énigme? Enquête sur les manuscrits, Turnhout, 2001, 10-11; F. S. Pedersen, The Toledan Tables. A Review of the Manuscripts and the Textual Versions with an Edition, København, 2002, I, 91-92; L. Moulinier-Brogi, Guillaume l’Anglais, le frondeur de l’uroscopie médiévale (XIIIe siècle), Genève, 2011, 188-190; C. P. E. Nothaft, Medieval Latin Christian Texts on the Jewish Calendar. A Study with Five Editions and Translations, Leiden-Boston, 2014, 495-497; O. de Solan, La réforme du calendrier aux conciles de Constance et de Bâle, Paris, 2016, 365-366.

24ra–⁠31vd	‘[b] Antiqua translatio sed incipit sic: Mundanorum ad hoc etc. Scientia namque astrorum ex te et ex illis est. Et non oportet peritum illorum iudicare secundum formam effectuum particularium… [a] Antiqua translatio Centilogii Ptholomei. Mundanorum ad hoc et ad illud mutatio corporum celestium… Dixit Ptholomeus: Iam scripsi tibi, Iesure, libros in Quadripartito de hoc quod scilicet quod operantur stelle in hoc seculo… Tertia translatio [title in the margin] Scientia stellarum etc. Doctrina stellarum ex te ex illis. Nec est doctrina in ea ut propheret… [c] Nova translatio. Scientia stellarum ex te et ex illis est. Astrologus non debet dicere res specialiter sed universaliter… Quod dixit Pt<olome>us, ex te et ex illis est, significat quod que res futuras prenoscere desiderat — [c] … et quanto melius quivimus exposuimus. Et sic finitur illud commentum Hali super Centilogio vel Centiloquio Ptholomei secundum antiquam et novam translationes… [d] … et si non ambulaverit rebellis est de eodem climate. Deo gracias. Finitus est ille textus Centiloquii in vigilia nativitatis Christi, similiter et commentum, 1444, prope horam … (?).’ = Abuiafar Hamet filius Joseph, 〈Commentum in Centiloquium〉 (‘Mundanorum’ version) (C.3.1.3) , with the beginning also given in Plato of Tivoli’s (C.3.1.1) and in Adelard of Bath’s (B.1.1) translations. The text is in three columns (a, b, c), with columns a and c written in smaller script. The organisation of the material on the first page (24r) is confusing, as are the titles given to each column. Column b gives the proposition of v. 1-3 in ‘Mundanorum’; column a repeats the proposition of v. 1 in ‘Mundanorum’, followed by Plato’s preface, v. 1 in Adelard’s translation and both the proposition and commentary of v. 2 in ‘Mundanorum’. Column c gives the proposition and commentary of v. 1 in Plato, followed by the proposition and commentary of v. 3 in ‘Mundanorum’. The pattern becomes clearer from the second page (24v) onwards, where column b consistently gives the proposition from ‘Mundanorum 1’ and columns a and c the proposition from ‘Mundanorum 2’ together with the commentary. The last two pages (31r-31v) are in four columns, but this hardly affects the pattern. No glosses. Corrections by the scribe.

24ra–⁠31vd

‘[b] Antiqua translatio sed incipit sic: Mundanorum ad hoc etc. Scientia namque astrorum ex te et ex illis est. Et non oportet peritum illorum iudicare secundum formam effectuum particularium… [a] Antiqua translatio Centilogii Ptholomei. Mundanorum ad hoc et ad illud mutatio corporum celestium… Dixit Ptholomeus: Iam scripsi tibi, Iesure, libros in Quadripartito de hoc quod scilicet quod operantur stelle in hoc seculo… Tertia translatio [title in the margin] Scientia stellarum etc. Doctrina stellarum ex te ex illis. Nec est doctrina in ea ut propheret… [c] Nova translatio. Scientia stellarum ex te et ex illis est. Astrologus non debet dicere res specialiter sed universaliter… Quod dixit Pt<olome>us, ex te et ex illis est, significat quod que res futuras prenoscere desiderat — [c] … et quanto melius quivimus exposuimus. Et sic finitur illud commentum Hali super Centilogio vel Centiloquio Ptholomei secundum antiquam et novam translationes… [d] … et si non ambulaverit rebellis est de eodem climate. Deo gracias. Finitus est ille textus Centiloquii in vigilia nativitatis Christi, similiter et commentum, 1444, prope horam … (?).’

= Abuiafar Hamet filius Joseph, 〈Commentum in Centiloquium〉 (‘Mundanorum’ version) (C.3.1.3)

, with the beginning also given in Plato of Tivoli’s (C.3.1.1) and in Adelard of Bath’s (B.1.1) translations. The text is in three columns (a, b, c), with columns a and c written in smaller script. The organisation of the material on the first page (24r) is confusing, as are the titles given to each column. Column b gives the proposition of v. 1-3 in ‘Mundanorum’; column a repeats the proposition of v. 1 in ‘Mundanorum’, followed by Plato’s preface, v. 1 in Adelard’s translation and both the proposition and commentary of v. 2 in ‘Mundanorum’. Column c gives the proposition and commentary of v. 1 in Plato, followed by the proposition and commentary of v. 3 in ‘Mundanorum’. The pattern becomes clearer from the second page (24v) onwards, where column b consistently gives the proposition from ‘Mundanorum 1’ and columns a and c the proposition from ‘Mundanorum 2’ together with the commentary. The last two pages (31r-31v) are in four columns, but this hardly affects the pattern. No glosses. Corrections by the scribe.